Real-time Trajectory Generation Research Articles

A Novel Learning-Based Trajectory Generation Strategy for a Quadrotor.

In this article, a learning-based trajectory generation framework is proposed for quadrotors, which guarantees real-time, efficient, and practice-reliable navigation by online making human-like decisions via reinforcement learning (RL) and imitation learning (IL). Specifically, inspired by human driving behavior and the perception range of sensors, a real-time local planner is designed by combining learning and optimization techniques, where the smooth and flexible trajectories are online planned efficiently in the observable area. In particular, the key problems in the framework, temporal optimality (time allocation), and spatial optimality (trajectory distribution) are solved by designing an RL policy, which provides human-like commands in real-time (e.g., slower or faster) to achieve better navigation, instead of generating traditional low-level motions. In this manner, real-time trajectories are calculated using convex optimization according to the efficient and accurate decisions of the RL policy. In addition, to improve generalization performance and to accelerate the training, an expert policy and IL are employed in the framework. Compared with existing works, the kernel contribution is to design a real-time practice-oriented intelligent trajectory generation framework for quadrotors, where human-like decision-making and model-based optimization are integrated to plan high-quality trajectories. The results of comparative experiments in known and unknown environments illustrate the superior performance of the proposed trajectory generation strategy in terms of efficiency, smoothness, and flexibility.

Real-time adaptive entry trajectory generation with modular policy and deep reinforcement learning

Recently, data-driven entry trajectory generation algorithms of hypersonic vehicles were highlighted for their high accuracy with low computational costs. Learning a unique black box model mapping the state to control variables is expected. However, insufficient adaptability remains a challenging problem when applying the algorithms in practice, especially for multi-missions. In this article, a real-time entry trajectory generation algorithm with modular policy is proposed to achieve adaptability to various missions, such as changing targets and emergency entry. Based on the modular idea, the entry trajectory problem is decomposed into two decision problems, i.e., adjusting the profile of the angle of attack (AOA) to determine the flight capability and planning the bank angle to ensure the satisfaction of task constraints, which correspond to AOA module and bank module respectively. Then, algorithms are developed by utilizing deep reinforcement learning (DRL) to train the two modules with which an intelligent entry trajectory generation algorithm is proposed to achieve real-time trajectory design in a wide range of reachable areas. Moreover, a non-uniform discretization approach with a state-related independent variable is proposed to deal with state misalignment and contradiction in stepsize settings. The simulation results demonstrate that the proposed algorithm can provide a reliable trajectory in a very short time and adapt to various tasks.

Position-attitude coupling guidance and control for asteroid landing with a flexible lander

Landing on an asteroid is a highly valuable endeavor accompanied by significant challenges, making it a promising area for further research. This paper aims to present a flexible lander specifically designed for asteroid landing missions while also studying the guidance and control techniques involved in its descent phase. Firstly, the paper briefly introduces the mission simulation model and asteroid environment from previous work. It then provides a detailed exposition on the guidance model which facilitates trajectory planning and the attitude control model used for managing the lander's attitude. The parametric trajectory is subsequently applied to obtain the position-attitude coupling trajectory that allows for the flexible lander's trajectory planning. The generating set search method is used to optimize the parametric trajectory under the appropriate constraints, ensuring high efficiency. In tracking the proposed trajectory, an open-loop control is applied for position tracking, while a closed-loop attitude controller is proposed for attitude control. An attitude control technique involving a combination of the nonsingular sliding mode control method with RBF to capture perturbations and unmodeled dynamics is adopted, and its global stability is proven using a Lyapunov-based approach. Monte Carlo simulation is conducted to test the performance of the proposed trajectory planning technique with results showing that real-time trajectory generation and refreshing are achieved. The feasibility and accuracy of the proposed guidance and control technique are further verified with another set of Monte Carlo simulation. Finally, the paper highlights one successful scenario including the descent and touching phases of asteroid landing with the flexible lander, illustrating its feasibility further.

GIS-Data-Driven Efficient and Safe Path Planning for Autonomous Ships in Maritime Transportation

Maritime transportation is vital to the global economy. With the increased operating and labor costs of maritime transportation, autonomous shipping has attracted much attention in both industry and academia. Autonomous shipping can not only reduce the marine accidents caused by human factors but also save labor costs. Path planning is one of the key technologies to enable the autonomy of ships. However, mainstream ship path planning focuses on searching for the shortest path and controlling the vehicle in order to track it. Such path planning methods may lead to a dynamically infeasible trajectory that fails to avoid obstacles or reduces fuel efficiency. This paper presents a data-driven, efficient, and safe path planning (ESP) method that considers ship dynamics to provide a real-time optimal trajectory generation. The optimization objectives include fuel consumption and trajectory smoothness. Furthermore, ESP is capable of fast replanning when encountering obstacles. ESP consists of three components: (1) A path search method that finds an optimal search path with the minimum number of sharp turns from the geographic data collected by the geographic information system (GIS); (2) a minimum-snap trajectory optimization formulation with dynamic ship constraints to provide a smooth and collision-free trajectory with minimal fuel consumption; (3) a local trajectory replanner based on B-spline to avoid unexpected obstacles in real time. We evaluate the performance of ESP by data-driven simulations. The geographical data have been collected and updated from GIS. The results show that ESP can plan a global trajectory with safety, minimal turning points, and minimal fuel consumption based on the maritime information provided by nautical charts. With the long-range perception of onboard radars, the ship can avoid unexpected obstacles in real time on the planned global course.

Real-time smooth trajectory generation for 3-axis blending tool-paths based on FIR filtering

Real-time smooth trajectory generation for 3-axis blending tool-paths based on FIR filtering

Trajectory Optimization of Chance-Constrained Nonlinear Stochastic Systems for Motion Planning Under Uncertainty

In this article, we present generalized polynomial chaos-based sequential convex programming (gPC-SCP) to compute a suboptimal solution for a continuous-time chance-constrained stochastic nonlinear optimal control (SNOC) problem. The approach enables motion planning for robotic systems under uncertainty. The gPC-SCP method involves two steps. The first step is to derive a surrogate problem of deterministic nonlinear optimal control (DNOC) with convex constraints by using gPC expansion and the distributionally robust convex subset of the chance constraints. The second step is to solve the DNOC problem using sequential convex programming for trajectory generation and control. We prove that in the unconstrained case, the optimal value of the DNOC converges to that of SNOC asymptotically and that any feasible solution of the constrained DNOC is a feasible solution of the chance-constrained SNOC. We also present the predictor–corrector extension (gPC-SCP <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\text{PC}$</tex-math></inline-formula> ) for real-time motion trajectory generation in the presence of stochastic uncertainty. In the gPC-SCP <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\text{PC}$</tex-math></inline-formula> method, we first predict the uncertainty using the gPC method and then optimize the motion plan to accommodate the uncertainty. We empirically demonstrate the efficacy of the gPC-SCP and the gPC-SCP <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\text{PC}$</tex-math></inline-formula> methods for the following two test cases: first, collision checking under uncertainty in actuation and physical parameters and second, collision checking with stochastic obstacle model for 3DOF and 6DOF robotic systems. We validate the effectiveness of the gPC-SCP method on the 3DOF robotic spacecraft testbed.

Real-time trajectory generation for dual-stage feed drive systems

Machine tools are designed using dual-stage feed drives with slow and fast stages when speed and accuracy must be delivered over large work-volume. The slow stage provides large-stroke positioning whereas the fast stage executes short-stroke accurate tool-tip placement. This paper presents a real-time trajectory generator (governor) that distributes reference motion commands so that coordinated high-speed dual-stage contouring motion can be realized. A novel dynamic command scaling (DCS) approach is developed to generate trajectories in real-time that fully utilize the stroke (range), velocity, acceleration and dynamic limits of the dual-stages drives. Demonstration in 2D laser patterning shows >2 times increase in productivity.

FEASIBLE AND OPTIMAL TRAJECTORIES GENERATION FOR AUTONOMOUS DRIVING VEHICLES, 11-24.

Real-time feasible and optimal trajectory generation subject tothe vehicle physical constraints, the surrounding obstacles, andthe environmental conditions is one of the most important partsof autonomous driving vehicles.

Online and Real-Time Trajectory Generation Method for Unforeseen Events Using a Modified Spline Approach

This letter focuses on the problem of online and instantaneous generation of smooth trajectories and their analytical time derivatives, where future reference signals provided by a trajectory planner or a user are a-priori unknown. For this purpose, we propose a modified cubic spline polynomial which transforms the instantaneous piecewise references into smooth and continuous functions for digital control systems. The resulting reference signals are not only smooth and continuous in time but also analytically differentiable. The inferred derivative values could then be used in a variety of linear and non-linear controllers such as, Proportional-Integral-Derivative (PID), sliding mode, and backstepping. We also provide optimum and boundary values for the parameters used in the proposed technique. In addition, we present a lightweight implementation (a few lines of code) of the algorithm by which real-time computations are rapidly performed using a microcontroller. Both simulation and real experiments demonstrate that for the plants having different degrees of complexities, the proposed approach with a PD / PID controller outperforms the conventional filtered derivative-based one in terms of overshoot in the step response, robustness against noise, and trajectory tracking error.

A Control Framework for Adaptation of Training Task and Robotic Assistance for Promoting Motor Learning With an Upper Limb Rehabilitation Robot

Robot-assisted rehabilitation has been a promising solution to improve motor learning of neurologically impaired patients. State-of-the-art control strategies are typically limited to the ignorance of heterogeneous motor capabilities of poststroke patients and therefore intervene suboptimally. In this article, we propose a control framework for robot-assisted motor learning, emphasizing the detection of human intention, generation of reference trajectories, and modification of robotic assistance. A real-time trajectory generation algorithm is presented to extract the high-level features in active arm movements using an adaptive frequency oscillator (AFO) and then integrate the movement rhythm with the minimum-jerk principle to generate an optimal reference trajectory, which synchronizes with the motion intention in the patient as well as the motion pattern in healthy humans. In addition, a subject-adaptive assistance modification algorithm is presented to model the patient’s residual motor capabilities employing spatially dependent radial basis function (RBF) networks and then combining the RBF-based feedforward controller with the impedance feedback controller to provide only necessary assistance while simultaneously regulating the maximum-tolerated error during trajectory tracking tasks. We conduct simulation and experimental studies based on an upper limb rehabilitation robot to evaluate the overall performance of the motor-learning framework. A series of results showed that the difficulty level of reference trajectories was modulated to meet the requirements of subjects’ intended motion, furthermore, the robotic assistance was compliantly optimized in response to the changing performance of subjects’ motor abilities, highlighting the potential of adopting our framework into clinical application to promote patient-led motor learning.

Real-time multi-quadrotor trajectory generation via distributed receding architecture and hierarchical planning in complex environments

Generation of multi-quadrotor trajectories in real-time in complex three-dimensional environments remains a grand challenge. Trajectory planning becomes computationally prohibitive as the number of quadrotors and obstacles increases. This paper proposes the distributed receding architecture-based hierarchical trajectory planning method (drHTP) to tackle this issue. The distributed receding architecture is established to formulate and solve a series of single-quadrotor short-horizon planning problems for reducing the computation complexity. In distributed planning, the time-heuristic priority mechanism is devised to assign a reasonable planning sequence to enhance the convergence performance. The hierarchical planning, including front-end initial trajectory generation and back-end trajectory optimization, is introduced for the single-quadrotor in each short horizon to further reduce the computation time. The sparse A* search algorithm is modified to only consider adjacent obstacles for obtaining the initial trajectory rapidly. The convergence of drHTP is analyzed theoretically. Numerical simulations with moving and dense obstacle scenarios are carried out to verify the effectiveness of drHTP. The comparative simulation results demonstrate that drHTP outperforms the state-of-the-art distributed sequential convex programming and distributed model predictive control methods in terms of computational efficiency. drHTP is also validated by the physical experiment in an indoor testbed.

Semi-Analytical Planetary Landing Guidance with Constraint Equations Using Model Predictive Control

With the deepening of planetary exploration, rapid decision making and descent trajectory planning capabilities are needed to cope with uncertain environmental disturbances and possible faults during planetary landings. In this article, a novel decoupling method is adopted, and the analytical three-dimensional constraint equations are derived and solved, ensuring real-time guidance computation. The three-dimensional motion modes and thrust profiles are analyzed and determined based on Pontryagin’s minimum principle, and a supporting semi-analytical reachability judgment method is presented, which can also be used to determine controllability. The algorithm is embedded in the model predictive control (MPC) framework, and several techniques are adopted to enhance stability and robustness, including thrust averaging, thrust correction after ignition, thrust reservation, and open-loop terminal guidance. Numerical simulations demonstrate that the proposed algorithm can guarantee real-time trajectory generation and meanwhile maintain considerable optimality. In addition, the MPC simulation shows that the algorithm can maintain a good accuracy under external disturbances.

A new real-time trajectory generation method modifying trajectory based on trajectory error and angular speed for high accuracy and short machining time

A computationally efficient FIR-filtering based tool-path (trajectory) modification method, which simultaneously realizes remarkable trajectory error reduction, vibration avoidance, and short machining time, is presented in this paper. Conventional trajectory generation in NC units causes trajectory error by using smoothing filters for limiting acceleration and avoiding vibration of the machines, and this trajectory error is often too large for practical applications. Therefore, a novel trajectory generation method is presented in this paper to remarkably reduce the trajectory error by modifying the trajectory commanded by G-codes on the basis of the trajectory error and angular speed. In order to realize the trajectory modification method, three key components, (i) p-corresponding method, (ii) ω-smoothing filter, and (iii) modification gain function, are developed in this study. The p-corresponding method is required to stably evaluate the trajectory error, while the other two components are used to compute appropriate modification gains for arbitrary trajectories. The proposed trajectory modification method is completed by integrating the components (i) to (iii), and it is verified utilizing a commercial machine tool. It is confirmed that average trajectory error is reduced remarkably by the proposed method without increasing machining time or sacrificing vibration avoidance by the smoothing filter. In particular, the trajectory errors at circular arcs are eliminated almost completely, e.g., the average trajectory error is reduced significantly by about 80% for a trajectory consisting of several circular arcs and corners.

An adaptive tracking control method for the all-wheel-driving and active-steering articulated vehicle with n-units

To achieve the running control of the all-wheel-driving and active-steering articulated vehicles (AWDASAVs) with n-units, an adaptive tracking control method is proposed in this paper, which includes a real-time target trajectory generation and an adaptive tracking control system. Firstly, the AWDASAV kinematics model is derived, and then the front-axle trace as the target trajectory is computed for all rear-axle steering by using data compressing and filtering, coordinate transformation, and local spline differences, which has small data storage and high computational efficiency and makes it easier to use in AWDASAV. Secondly, an adaptive tracking control system composed of an adaptive active steering controller and a differential distribution controller is designed to achieve accurate trajectory tracking and coordinated movement for AWDASAV. Finally, the AWDASAV simulation model with five-units was built in ADAMS by code development for cross-validation simulation, and the simulations with two cases at various speeds are carried out to verify the simulation model and control method. To further investigate the proposed method, the influence of three parameters on the tracking control performance and comparison with different control methods are carried out. The results exhibit excellent tracking control performance.

Continuous trajectory planning based on learning optimization in high dimensional input space for serial manipulators

In order to generate trajectories continuously for serial manipulators with high dimensional degrees of freedom (DOFs) in a dynamic environment, a real-time trajectory planning method based on optimization and machine learning aimed at high dimensional inputs is presented. A learning optimization (LO) framework is established. Multiple criteria are defined to evaluate the performance quantitatively, and implementations with different sub-methods are discussed. In particular, a database generation method based on input space mapping is proposed for generating valid and representative samples. The methods presented are applied on a practical application—haptic interaction in virtual reality systems. The results show that the input space mapping method significantly elevates the efficiency and quality of database generation and consequently improves the performance of the LO. With the LO method, real-time trajectory generation with high dimensional inputs is achieved, which lays the foundation for robots with high dimensional DOFs to execute complex tasks in dynamic environments.

PSO-Based Soft Lunar Landing with Hazard Avoidance: Analysis and Experimentation

The problem of real-time optimal guidance is extremely important for successful autonomous missions. In this paper, the last phases of autonomous lunar landing trajectories are addressed. The proposed guidance is based on the Particle Swarm Optimization, and the differential flatness approach, which is a subclass of the inverse dynamics technique. The trajectory is approximated by polynomials and the control policy is obtained in an analytical closed form solution, where boundary and dynamical constraints are a priori satisfied. Although this procedure leads to sub-optimal solutions, it results in beng fast and thus potentially suitable to be used for real-time purposes. Moreover, the presence of craters on the lunar terrain is considered; therefore, hazard detection and avoidance are also carried out. The proposed guidance is tested by Monte Carlo simulations to evaluate its performances and a robust procedure, made up of safe additional maneuvers, is introduced to counteract optimization failures and achieve soft landing. Finally, the whole procedure is tested through an experimental facility, consisting of a robotic manipulator, equipped with a camera, and a simulated lunar terrain. The results show the efficiency and reliability of the proposed guidance and its possible use for real-time sub-optimal trajectory generation within laboratory applications.

Time-Continuous Real-Time Trajectory Generation for Safe Autonomous Flight of a Quadrotor in Unknown Environment

In this paper, we present an efficient global and local replanning method for a quadrotor to complete a flight mission in a cluttered and unmapped environment. A minimum-snap global path planner generates a global trajectory that comprises some waypoints in a cluttered environment. When facing unexpected obstacles, our method modifies the global trajectory using geometrical planning and closed-form formulation for an analytical solution with 9th-order polynomial. The proposed method provides an analytical solution, not a numerical one, and it is computationally efficient without falling into a local minima problem. In a simulation, we show that the proposed method can fly a quadrotor faster than the numerical method in a cluttered environment. Furthermore, we show in experiments that the proposed method can provide safer and faster trajectory generation than the numerical method in a real environment.

Real-Time Four-Dimensional Trajectory Generation Based on Gain-Scheduling Control and a High-Fidelity Aircraft Model

Aircraft ground movement plays a key role in improving airport efficiency, as it acts as a link to all other ground operations. Finding novel approaches to coordinate the movements of a fleet of aircraft at an airport in order to improve system resilience to disruptions with increasing autonomy is at the center of many key studies for airport airside operations. Moreover, autonomous taxiing is envisioned as a key component in future digitalized airports. However, state-of-the-art routing and scheduling algorithms for airport ground movements do not consider high-fidelity aircraft models at both the proactive and reactive planning phases. The majority of such algorithms do not actively seek to optimize fuel efficiency and reduce harmful greenhouse gas emissions. This paper proposes a new approach for generating efficient four-dimensional trajectories (4DTs) on the basis of a high-fidelity aircraft model and gain-scheduling control strategy. Working in conjunction with a routing and scheduling algorithm that determines the taxi route, waypoints, and time deadlines, the proposed approach generates fuel-efficient 4DTs in real time, while respecting operational constraints. The proposed approach can be used in two contexts: ① as a reactive decision support tool to generate new trajectories that can resolve unprecedented events; and ② as an autopilot system for both partial and fully autonomous taxiing. The proposed methodology is realistic and simple to implement. Moreover, simulation studies show that the proposed approach is capable of providing an up to 11% reduction in the fuel consumed during the taxiing of a large Boeing 747-100 jumbo jet.

셀프-밸런싱 역진자 로봇에 대한 모델기반 실시간 궤적생성 방법

When a two-wheeled self-balancing mobile robot performs a rapid speed change, the nonlinear characteristic of the inverted pendulum dominates the pitch motion, and maintaining the postural stability becomes difficult when using a conventional linear controller only. Hence, in order to ensure agility and mobility in addition to postural stability during an acceleration or deceleration phase, an appropriate reference trajectory for the velocity and pitch control loop is needed in place of the typical step reference input. In this paper, we propose a real-time trajectory generation method for the underactuated self-balancing robot based on solving the nonlinear equation of motion, considering the dynamic characteristics, and applying numerical approximations. The effectiveness of the proposed planning scheme was confirmed through comparative simulations and experiments.

Real-Time Trajectory Generation and Reachability Determination in Autorotative Flare

Autorotation maneuvers inherently offer little margin for error in execution and induce high pilot workload, particularly as the aircraft nears the ground in an autorotative flare. Control augmentation systems may potentially reduce pilot workload while simultaneously improving the likelihood of a successful landing by offering the pilot appropriate cues. This paper presents an initial investigation of a real-time trajectory generation scheme for autorotative flare based on time-to-contact theory. The algorithm exhibits deterministic runtime performance and provides a speed trajectory that can be tracked by a pilot or inner-loop controller to bring the vehicle to a desired landing point at the time of touchdown. A low-order model of the helicopter dynamics in autorotation is used to evaluate dynamic feasibility of the generated trajectories. By generating and evaluating trajectories to an array of candidate landing points, the set of reachable landing points in front of the aircraft is determined. Simulation results are presented in which the trajectory generator is coupled with a previously derived autorotation controller. Example cases and trade studies are conducted in a six degree-of-freedom simulation environment to demonstrate overall performance as well as robustness of the algorithm to variations in target landing point, helicopter gross weight, and winds. The robustness of the reachability determination portion of the algorithm is likewise evaluated through trade studies examining off-nominal flare entry conditions and the effects of winds.